Solve for $k$, $ -\dfrac{6}{5k + 5} = \dfrac{5k - 7}{10k + 10} + \dfrac{6}{25k + 25} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $5k + 5$ $10k + 10$ and $25k + 25$ The common denominator is $50k + 50$ To get $50k + 50$ in the denominator of the first term, multiply it by $\frac{10}{10}$ $ -\dfrac{6}{5k + 5} \times \dfrac{10}{10} = -\dfrac{60}{50k + 50} $ To get $50k + 50$ in the denominator of the second term, multiply it by $\frac{5}{5}$ $ \dfrac{5k - 7}{10k + 10} \times \dfrac{5}{5} = \dfrac{25k - 35}{50k + 50} $ To get $50k + 50$ in the denominator of the third term, multiply it by $\frac{2}{2}$ $ \dfrac{6}{25k + 25} \times \dfrac{2}{2} = \dfrac{12}{50k + 50} $ This give us: $ -\dfrac{60}{50k + 50} = \dfrac{25k - 35}{50k + 50} + \dfrac{12}{50k + 50} $ If we multiply both sides of the equation by $50k + 50$ , we get: $ -60 = 25k - 35 + 12$ $ -60 = 25k - 23$ $ -37 = 25k $ $ k = -\dfrac{37}{25}$